“I knew it was happening of course,” Kardashian, 33, says, “but I didn’t know it would be the cover. I’m just so honored.”

Kardashian says the photo shoot was so top secret she didn’t even tell her sisters. “They were a little suspicious,” she says. “My mom knew because we used part of her house, but I told them it was something for Kanye. I don’t keep the best secrets.”

As for daughter North, 9 months, the close-up in the family photo on the couch had a little complication. “North peed on Kanye in that shot,” reveals Kardashian. “He was trying to tell me. I had to get up and clean him off.”

Despite mixed reviews, Kardashian says they’re just proud to be trailblazers. “Kanye’s the first rapper, I’m the first reality star, we’re the first interracial couple,” she says.

Another thing the Keeping Up with the Kardashians star loved: the designer gowns she tried on, including the strapless Lanvin she dons on the cover. “I felt like the real-life Carrie Bradshaw.”

The cover spread was a long time in the making for Kardashian, whose sister Kendall Jenner generated cover buzz first.

As recently as a month ago, two industry insiders dished doubts to PEOPLE that the new mom would make the cover any time soon.